# How Credit Card Companies Sell A Loan

Almost all of us who have been working for a couple of years own a credit card. Some perhaps more than one, each tailored for a particular purpose like online shopping, paying bills, groceries, etc. That’s what a YouGov survey says anyway. Thankfully, it also says that few Singaporeans are in debt because of credit cards, which is a good thing.

But I am sure we have all heard the story. Spent too much in a particular month on a fancy new item, could not afford to pay back. Owe them money and soon the interest itself spirals out of control. How does this all happen? Well, the first truth is this – that is exactly how credit card companies make their money. Each time they allow a credit card user to pay on credit, they are taking a risk. A risk that the user may not pay back in full or in a worse case, go bankrupt and default on his payment. So the interest that is being charged in the event of late or non-payment is to compensate the credit card company for the risk that they are taking on. So if you are the type of credit card user that always pays your credit card bills on time, then you are not the kind of client that they actually want, because aside from the annual credit card fees (which are usually waived), they do not really earn that much from you. What they really earn from is the interest.

I will not go too much into the late payment fees, because those are pretty crazy rates (26.9% p.a.) we are looking at and not too interesting. Instead, I will discuss the other way that they entice people to borrow from them – take out a credit card loan in as painless a way as possible. Here is an example of the kind of advertisement I constantly get from Citibank, just because I own a credit card with them.

The obvious question that stands before us is: What is the difference between 4.55% p.a. and EIR 8.50% p.a.? Before we answer that question, first we must know what EIR stands for. It is short for Effective Interest Rate, which reflects the true cost of a loan and uses the following formula:

$EIR = (1 + \frac{i}{n})^n - 1$, where $i$ is the nominal interest rate (stated rate associated with a loan, but not what a borrower is paying) and $n$ is the number of periods (usually in months or years).

So why are there two numbers? Well, 4.55% p.a. here refers to the nominal interest rate. I’ll demonstrate this with a bit of math, assuming that I’m borrowing $1,000 over 36 months and counting backwards using the monthly instalment of$31.57 as shown below.

In 36 months, the total amount paid is $\char36 31.57 \times 36 = \char36 1,136.52$.
As a percentage of the original loan, that is $\char36 1,136.52 \div \char36 1,000 \times 100\% = 113.652\%$.
Averaged over 3 years, that is $\frac{113.652\% - 100\%}{3} = 4.55\%$ per annum.
But like I said above, that’s not really how you should understand interest rate. Instead, we need to look at the EIR by understanding at the T&Cs and the mortization table to get a sense of its effects:

So look at the T&Cs clause 12 and you will find a formula for calculating the interest component of each monthly statement, which uses the formula $EIR \times outstanding\;unbilled\;Program\;amount \div 12 [months]$.

Rather than work out the EIR, let’s get a feel of it by working out an example after paying the first instalment of $25.65, with principal paid$24.49 and interest paid \$1.16. So that means the outstanding unbilled Program amount is $\char36 1,000 - \char36 24.49 = \char36 975.51$,
and the interest component for the next monthly instalment is $\frac{8.5\% \times \char36 975.51}{12} = \char36 6.91$, rounded up to 2 decimal places.

The basic idea is this: The higher your EIR, the more you interest you are paying much earlier in the instalments and that’s the true interest that you are being charged for the remaining principal that you still owe after borrowing. In other words, unless you can guarantee that you can find an investment that earns at a rate higher than the EIR with the amount you borrowing, then forget about it.

I hope this post gives you a better sense of the size of the hole you are digging when you decide to borrow from the credit card companies, banks or any financial institution for that matter. They can always easily fudge the numbers by showing you the smaller nominal interest rate which only represents the total interest you pay over the course of the loan tenor. So be clear what the numbers actually mean before you make your financial decision and make sure it makes sense!